Suppose angle of depression from top of the tower to point A is 45°. And height of tower is 10 m. What is the distance of point A from the building?
Let building be BC
So, angle of depression from point B is 45°
and Height = BC = 10 m
BX is the horizontal
Now, we need to find the distance of point A from the building
Now, lines BX and AC are parallel,
and AB is the transversal
So, Alternate angles are equal
∴ ∠ BAC = ∠ XBA
∴ ∠ BAC = 45°
Now, we need to find base AC
And we are given height 10 m.
So, we can use tan
As
tan A = Side opposite to angle A / Side adjacent to angle A
tan 45° = BC / AC
1 = 10/ AC
AC = 10 m
∴ Distance AC is 10 m